The Beagles (1966 cartoon)
From Rocklopedia Fakebandica
self-titled show. Actually, Beatle-esque is too generous. I would say Chad & Jeremy-esque or maybe Peter & Gordon-esque. Stringer and Tubby were the pooches in question. Although they were cancelled from CBS after a year (and were re-run on ABC the next year), they lasted long enough to release an album, Here Come The Beagles.